Rupert Murdoch's Sun newspaper likes to back election winners -- from Margaret Thatcher to Tony Blair. Whether exaggerated or not, the billionaire's influence has been credited with victories for both right and left.

Sun's circulation

1.7 million

But the Sun's call on Tuesday for Britons to vote in favor of leaving the European Union will test Murdoch's influence against social media -- and Facebook in particular.

Murdoch's newspaper readership is waning: The Sun's average monthly circulation, while still bigger than the competition, has fallen by 42 percent in six years to 1.7 million readers. The Times -- Murdoch's other, more highbrow property -- has a circulation of about a quarter of that.

Setting Sun

Average monthly circulation of Rupert Murdoch's U.K. newspaper The Sun has almost halved in six years

Source: ABC data

Since its separation from Murdoch's film and television businesses in June 2013, News Corp.'s stock has languished. And advertisers are increasingly diverting their dollars to social media over newspapers.

Rising Star

News shares have trailed Facebook since the newspaper publisher split from Murdoch's film & TV unit

Source: Bloomberg

Meanwhile, Facebook, which has only been in existence for little longer than a decade, has a British user base of more than 30 million -- and more than half the U.K. population will sign on to the platform at least once this year, according to eMarketer.

Wide Reach

More than half the UK population will sign on to Facebook at least once this year

Source: eMarketer

Facebook has become a powerful force in the media business: prominent placement of a story in a user's news feed sends a fire-hose of users to websites, giving Mark Zuckerberg's algorithm tremendous sway over what gets read and seen and what disappears into oblivion. With the advent of Facebook Live, which allows anyone to post live video feeds, the site is attempting do to TV news what it has already done to print: disrupt it.

Where does Brexit come in?

Firstly, both campaigns are using the platform to drum up support: Vote Leave's Facebook page has 487,559 likes -- fractionally more than the Remain campaign's 474,409 likes.

But when it comes to news, Zuckerberg portrays Facebook as an agnostic, neutral platform for everyone's views, unlike the old press barons who relished in issuing election endorsements and courting politicians. The algorithm decides the placement of news stories, and it has no bias, says Zuckerberg.

But the weaknesses in that argument were exposed last month after Gizmodo alleged Facebook's team of human editors downplayed reports on conservative websites. Zuckerberg pledged not to use Facebook's power to sway elections -- but the fact remains that no one really knows what the company is doing with its algorithm and influence. He's asking us to trust him.

One thing is clear, beyond just disseminating news, Facebook can mobilize voters. On June 3, the website reminded U.K. users that the deadline to register for the referendum was fast approaching. When the company did the same in Britain's general election last year, it sparked a surge in voter registrations -- especially amongst young people. And that's the section of the U.K. population that leans most towards the remain camp.

The Facebook Effect

Voter registration surged, particularly among young people, after a Facebook reminder

Source: UK government data

Polls put the outcome of the referendum on a knife-edge. If the U.K. does vote to remain, those looking to find the wisdom of the crowd might want to look to Facebook over Murdoch.

This column does not necessarily reflect the opinion of Bloomberg LP and its owners.